The National Science Foundation (NSF) awarded a $299,877 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to Yale University. The three-year grant, effective August 1, 2024, will support research in two primary areas: 1) Proving new formulas for solutions to Einstein's equation describing the geometry and curvature of space-time, and 2) Studying two-dimensional scale invariant systems through simplifying approaches to enable exact solutions. The research aims to bridge mathematics and high-energy physics, with plans to broadly disseminate findings and train graduate students. Additionally, the grant will enable a direct attack on proving a conjectural picture of the hyperkahler geometry of moduli spaces of Higgs bundles, as well as numerical studies of the hyperkahler metric. The project also involves developing a new abelianization technique to construct conformal blocks for certain vertex algebras.
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